Planck scale from broken local conformal invariance in Weyl geometry

Abstract

We show that in a quadratic gravity based on Weyl's conformal geometry, the Planck mass scale can be generated from quantum effects of the gravitational field and the Weyl gauge field via the Coleman-Weinberg mechanism where a local scale symmetry is broken. At the same time, the Weyl gauge field acquires a mass less than the Planck mass by absorbing the scalar graviton. The shape of the effective potential is almost flat owing to a gravitational character and high symmetries, so our model would provide for an attractive model for the inflationary universe. We also present a toy model showing spontaneous symmetry breakdown of a global scale symmetry by moving from the Jordan frame to the Einstein one, and point out its problems.